The general theory of relativity (GR) is an impeccably robust
relativistic theory of gravity.
It forms the basis for our understanding of gravitational phenomenon at
small as well as large scales
[1]}, [2]}.
However, it is well known that GR cannot be the ultimate theory of
gravitation since it
has a well defined regime of validity; for example, understanding past
and future spacetime
singularities are beyond the reach of GR.
Suitable modification(s) of GR is(are) essential to understand
singularities,
or to resolve them. It is believed that a quantum theory of gravity may
lead to solution
to the problems affecting GR [2]}, [4]}, [5]}, [6]}, [7]}.
Naturally, in absence of any consensus on the theory of quantum gravity,
modified
theories of gravity with quantum corrections are also of interest.
The Einstein- Hilbert action may be thought of as only a low energy
contribution
and higher curvature terms consistent with the diffeomorphism invariance
may become
relevant as one goes to higher energies. Higher curvature corrections
should leave imprints
at low energy scales which become important for low energy physics
too [6]}, [7]}, [10]}.
Out of these alternate theories, we shall study the \(f(R)\)  model
since it has been found interesting in the cosmological studies as well.
These \(f(R)\)  gravity models are thought of as alternate
to the dark energy models [11]}, [12]}, [13]}.
The standard way to construct these \(f(R)\)  theories
is to replace the Einstein- Hilbert Lagrangian
by a well defined function of Ricci scalar, \(f(R)\) 
(for general relativity \(f(R)=R\) ) [14]}.
For a detailed review of
the motivation, validity of various functional forms \(f(R)\) ,
applications as well as shortcomings of
these gravity theories have
been extensively analyzed [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}.
